Descriptive Geometry in England — a Historical Sketch

Oral presentations 805 Descriptive Geometry in England — aHistoricalSketch Snezana LAWRENCE Simon Langton Grammar School for Boys, Canterbury, Kent CT4 7AS, UK snezana [email protected] Abstract History of Descriptive Geometry in France and its utilisation in the French educational system since the 18th century has already been well documented in the work of Taton (1951), and more recently Sakarovitch (1989, 1995). The history of the technique in England, however, makes a captivating story, particularly as it relates not only to the technique itself, or how the treatises relating to it were translated into English, but because it was also closely related to the establishment of the architectural and engineering professions in Britain. The technique of Descriptive Geometry was invented by Gaspard Monge1 in or around 1764, when Monge, as part of his everyday work duties at the at l’Ecole´ Royale du Génie de Mézières,2 was given the task of determining the plan of defilement in a design of fortification. His invention was deemed so ingenious, and so useful in military engineering, that it was proclaimed a military secret. The scenarios of what ‘might have been if’3 would be interesting to consider here, for the technique was not published until the end of the century, and until Monge himself became involved in setting up the institutions of the new Republic during the Revolution.4 The new educational institutions of the Republic defined the ways in which mathematics, engineering and architecture and their communications were to be conducted. Descriptive Geometry was one such revolutionary subject, as Sakarovitch (1995) pointed out: Ascholasticdisciplinewhichwasborninaschool,byaschoolandforaschool(but maybe one should say in the Ecole´ Polytechnique, by the Ecole´ Polytechnique, and for the Ecole´ Polytechnique), descriptive geometry allows the passage from one process of training by apprenticeship in little groups which was characteristic of the schools of the Ancien Regime, to an education in amphitheatres, with lectures, and practical exercises, which are no longer addressed to 20 students, but 1Gaspard Monge, (1746–1818), born in Beaune, died in Paris, France. Monge is most famous for his invention of Descriptive Geometry and for his work on the application of analysis to geometry. See Taton (1951), Sakarovitch (1989, 1995 and 1997). 2The Royal School of Engineering at Mézičres was founded in 1748 and was closed in 1794 when it transferred to the School of Engineering at Metz. 3Some ‘ifs’ might be: what if Monge did not become so prominent in the New Republic, setting up the institutions such as Ecole´ Polytechnique and Ecole´ Normale Supérieure which provided the setting for the teaching of Descriptive Geometry; what would have happened if Monge died during the Terror; or what would have happened if indeed no one looked seriously at the technique as it was invented by, at the time, a lowly clerk in the drafting office of a famous engineering school. 4Monge was one of the first teachers at Ecole´ Normale Supérieure and one of the founders of the Ecole´ Polytechnique. 806 Snezana LAWRENCE to 400 students. Descriptive geometry also stems from revolutionary methods. Ameanstoteachspaceinanaccelerated way in relation to the former way of teaching stereotomy, an abstract language, minimal, rapid in the order of stenography, descriptive geometry permits a response to the urgent situation as for the education of an elite, which was the case of France at the moment of the creation of the Ecole´ Polytechnique.5 Figure 1 – Plate one from Géométrie Descriptive, Paris An VII (1799) The further historical development of Géométrie Descriptive in France has been well documented in the work of Taton (1951), Sakarovitch (1989, 1995, 1997), and Guinness (1990). However, little has been known so far of the fate Descriptive Geometry met upon its translation into English. The scarcity of information and references to it in the contemporary practices in English mathematics education leaves room for contemplation that led to this publication. In fact, the first treatise on descriptive geometry in English language was first published by a former pupil of Monge, Claude Crozet, who found a place teaching the subject at the newly founded military academy at West Point, US.6 Unknown to the British public for some decades, this book was in England preceded by a series of treatises on the orthographic projection published by, mainly, an architectural writer, who described himself as an ‘architect andamathematician’,PeterNicholson7.Notably, 5Sakarovitch (1995), p. 211. 6Claude Crozet (1790–1864) wrote ATreatiseonDescriptiveGeometryin 1821 for the use of cadets at the Military Academy at West Point US. Crozet was born in Villefranche, France and was educated at Ecole´ Polytechnique. He emigrated to the United States in 1816 and on the recommendation of Lafayette and Albert Gallatin, was appointed on 1st of October 1816, the assistant professor of engineering at West Point Academy and on 6th of March 1817 professor and head of the department. 7Peter Nicholson (1765–1844) was born in Prestonkirk, East Lothian on 20th July 1765, a son of a stonemason. His mathematical writings are mainly to be found in three papers and two books: 1817 – An Introduction to the Method of increments;1818–Essay on the Combinatorial Analysis;1820–Essay on Involution and Evolution.Hisbooksonmathematicswere:1823–A popular Course of Pure and Mixed Mathematics and in 1824 – APracticalSystemofAlgebra.Thelistofhisarchitecturalopusislengthierand not of concern for this paper. Oral presentations 807 technique very similar to that of descriptive geometry appeared almost fully explained in Nicholson’s Treatise on stone-cutting in 1823.8 Nicholson’s Treatise on Projection,published in 1840 set out his technique in detail. This became accepted and known as the ‘British system of orthographic projection’9 and was republished many times during the 19th century in the works of Binns and Bradley, although without the reference to its inventor.10 Figure 2 – Plate 1 from Nicholson’s Treatise,London:1840 Géométrie Descriptive ‘proper’ was translated into Spanish in 1803, and into English in 1809, presumably for military purposes, as therearenopublicationstobefoundinEnglish libraries to suggest that the work was made public. No complete work on the subject appeared in English until 1841, when Rev. T. G. Hall of King’s College,London,published The Elements of Descriptive Geometry, chiefly designed for students in Engineering,which mentioned Thomas Bradley as the first one to give lectures on Descriptive Geometry, at the Engineering Department of King’s College in London. This treatise was succeeded by a few treatises all of which were published for the English military academies11,andallofwhichwerethestraightforwardtranslationsoftheoriginal technique. According to the records in the British Library, it would seem that the last of these treatises was one published by Heather of the Woolwich Military Academy in 185112. However, treatises continued to be published in England until the end of the 19th century with ‘Descriptive Geometry’ in their titles, but very little of the original technique can be found in them; these treatises were mainly based on the system invented and described by Peter Nicholson. 8See Nicholson, (1822) p. 45. 9See Grattan-Guinness, I. and Andersen, K. (1994). 10See bibliography. 11They were published for the Military Academy schools at Woolwich and at Portsmouth. 12See Heather (1851). 808 Snezana LAWRENCE In order to understand the reasons for this state of affairs, let us turn to the develop- ments related to the mathematics education, and in particular the education geared for the architectural and the engineering professionswhichwouldhavebeentheprimaryusersof any such technique. The translation of descriptive geometry into English was contemporary with the chang- ing nature of educational politics in England. English were, at the time, discussing and taking steps to improve the provision of education for the poor and the working class, not least because the need for an educated and trained working force became obviously needed by the rise of the modern concepts of the building professions — the engineering and the architectural. At the same time, with the adoption of the concept of profession, the craftsman and the professional became differentiated to such an extent that a need for a clear and easily trans- missible system of communication between thetwobecameanurgentissue.Thefirstand foremost problem was that of inventing a new principle of graphical communication. Such a ‘language’ needed to satisfy two most important prerequisites: it had to be easily transmissi- ble, and it had to be standardised, to allow usage across the territory for which it was valid.13 Up to and during the greater part of the 18th century, the geometrical techniques em- ployed by craftsmen and designers were empirical recipes,14 they offered no underlying principle of unity by which the similar processes of defining and executing the methods of stone- cutting could be transferred from one case to another. These techniques often resembled a catechism rather than an exact method. Furthermore, geometrical methods, both graphical and constructive,15 were in the 17th and 18th centuries expounded in treatises on the art of stone-cutting; they were mainly based on what authors found from the sources still surviving within the operative masons’ craft, and were deeply coloured by the mythology pertaining

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